BEIRUT—Syria's regime recaptured a town near Damascus from Islamist rebels and attacked other rebel-held areas, fanning fears among some in the opposition that President Bashar al-Assad is gaining advantage from the U.S.-led air campaign against Islamic State militants.

Syrian military officers, speaking on state television, said their forces and an allied militia drove the al Qaeda-linked Nusra Front and other rebels from Adra al-Umaliya after nearly a year of fighting over the town. State television touted it as a major...